Special Report: Seeking a New World : Case Study / Emigration : Third World Woes Forcing a New Exodus : Around the globe, leaving home is the only response to problems seemingly too numerous to overcome.

CAIRO — Ahmed Fakhr, a career military officer who risked his life for Egypt in three wars, sat back in his chair and paused. The words were clearly difficult. "Fifteen years ago, I used to tell my two boys, if you leave this country and go work abroad, you are betraying your national cause. Stay here. Develop Egypt. The government paid for your health care, for your education. Stay here ."

Fakhr sighed, then shrugged. "Today, I am preparing my two boys to emigrate," he said. "It's a question of the resources available, and the population."

In Egypt, a country overwhelmed by a million new mouths every nine months, leaving has long been a response to an economy unable to keep up with an exploding population. But its desperation is reaching new heights, and similar despair is evident in many other countries.

Like a global game of musical chairs, the world is witnessing the uprooting of tens of millions of people as factors once unique to countries like Egypt--economic misery, uncontrolled growth and limited space--spur an unprecedented human exodus.

"This is likely to be the biggest movement of humanity in world history," said Doris Meissner, former commissioner of the Immigration and Naturalization Service. "All corners of the globe will be affected, directly and because of the rippling-down effect."

The list seems endless: Soviet Jews to Israel. Vietnamese to Hong Kong and Hong Kong Chinese to Australia, Bolivia, Canada, Belize or Singapore. Moroccans, Tunisians and Algerians to France, Spain and Italy. Burmese to Thailand; Mozambicans to Malawi. Afghans to Pakistan and Iran. East Europeans to West Europe. Filipinos and Gypsies to any place that will take them.

The United States is hardly exempt. Although only a few of the vast numbers who want to emigrate there make it, the total still is enough to change the American complexion. In the 21st Century, white descendants of European settlers will become a minority--reflecting the effects of immigration and higher birthrates among blacks and Latinos.

The change in other countries will be just as dramatic. Birth control in the West and Japan is creating aging societies and shortages of younger laborers, while developing nations produce more people than they can ever hope to accommodate, further fueling emigration.

But the two countervailing trends are unlikely to neatly cancel each other out. Indeed, the world's widening demographic imbalance and the momentous flow of humanity will be among the most divisive and destabilizing issues of the 21st Century.

Immigration already is emerging as a powerful political issue, contributing to resurgent racism and nativism, providing a tempting target for right-wing movements and producing a sharper international division between North and South.

Although it cannot be calibrated precisely, emigration appears to be growing exponentially.

"In the past 10 years, since 1980, we've seen at least a doubling of the pool of people seeking access to other countries," said David Simcox, director of the Center for Immigration Studies in Washington. "And that's a conservative estimate."

Many specialists predict that emigration could double again by 2000, especially with political upheavals worldwide.

The Soviet empire's possible collapse could trigger a massive exodus. More than 500,000 Soviets left this year after exit permit requirements were scrapped; between 7 million and 20 million are expected to leave in the 1990s. One million have applied for U.S. residence--more than the total number of Soviet emigres bound for all destinations since World War II.

In South Africa, the anticipated end of apartheid has led thousands of whites to apply for the British citizenship of their ancestors. As Hong Kong nears the 1997 transfer of sovereignty from Britain to China, 1,000 already are leaving weekly.

Closer to home, 22% of Mexicans who participated in a 1989 Times Mirror poll said they were likely to move to the United States--a figure comparable to the number of North Africans and East Europeans who would like to get into Western Europe.

The new human wave underscores a shift from previous eras. In the postwar period, most emigrants sought refuge from political oppression or conflicts; today, the main motive is economic, often the byproduct of population growth.

But doors are rapidly closing in front of them as the world runs out of inhabitable frontiers. Many industrialized nations no longer want the developing world's demographic overflow--the largely unskilled workers once welcomed to foster industrialization. Australia and Canada, which once encouraged immigration, have begun to limit refugees and unskilled laborers, particularly Southeast Asians, in favor of skilled immigrants.